matrices – Checking if a given matrix is orthogonal

Given an orthogonal matrix

$A=
begin{pmatrix}
1 & 1 & 1 &1 \
1 & 1 & -1 &-1\
1 & -1 & 0 &0\
0 &0&1&-1
end{pmatrix}
$

then values of $[AA^{T}]^{-1}$ is ?

My question is how come it is an orthogonal matrix $1^2+1^2+1^2+1^2ne1$

Sum of squares of rows should be one isnt it?